OFFSET
1,2
COMMENTS
An unlabeled rooted tree is fully recursively anti-transitive if no proper terminal subtree of any terminal subtree is a branch of the larger subtree.
EXAMPLE
The sequence of fully recursively anti-transitive rooted trees together with their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
7: ((oo))
8: (ooo)
9: ((o)(o))
11: ((((o))))
16: (oooo)
17: (((oo)))
19: ((ooo))
21: ((o)(oo))
23: (((o)(o)))
25: (((o))((o)))
27: ((o)(o)(o))
31: (((((o)))))
32: (ooooo)
35: (((o))(oo))
49: ((oo)(oo))
51: ((o)((oo)))
53: ((oooo))
57: ((o)(ooo))
59: ((((oo))))
63: ((o)(o)(oo))
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
fratQ[n_]:=And[Intersection[Union@@Rest[FixedPointList[Union@@primeMS/@#&, primeMS[n]]], primeMS[n]]=={}, And@@fratQ/@primeMS[n]];
Select[Range[100], fratQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved